by Kareem Carr

Bottom line: These are a few simple tips for using your mathematical skills in jobs and research opportunities outside of mathematics.

For this article, I decided to discuss something that is probably of relevance to many people at this point in the year, but on which I cannot give the final word as I am still learning myself: job hunting. Specifically, I want to talk about ways in which mathematicians can promote themselves to non-mathematicians either for employment or for collaboration. I hope that some of you, readers, will give your opinions. I will summarize my experiences into a few simple rules:

1. **Learn how to listen.** Do not ignore what people are telling you about what they think is important about their problem and what they want you to solve. Imagine trying to use a calculator or computer that always wanted to have a debate with you about the worth of computing a result before it would compute it. It would be unpleasant and tedious. While I am not saying that you should view yourself as merely a tool, you should realize that most people are coming to mathematics as consumers.

2. **Learn how to talk.** When asked to do something, the best answer is a firm, business-like yes or no and a firm estimate on how long it will take. If you can’t give an answer like that, the next best answer is to say exactly how long it will take you to get to a place where you can give a firm yes or no. It’s typical to add caveats in academia but in real life it turns a lot of people off.

3. **Learn how to shut-up.** What you absolutely should not do unless specially asked, is go into extraordinary detail about how you will get things done. Even when asked, it’s best to err on the side of fewer more general details and as little about the nature of the calculations as possible.

4. **Learn what to do in disagreement.** Sometimes, your advice or standard of rigor will be disregarded. It’s important to realize other fields and arenas of life have different standards of proof. I think it helps to sort out what you want to do in this situation before it happens. If you can’t get past this issue, using your mathematical skills in this way might not be for you.

5. **Learn how to program.** It’s a good idea to be able to automate some of your work. The more automated it is, the more likely others will use it.

6. **Learn how to learn** (things that aren’t mathematics). This can be unpleasant (for some) but is often absolutely necessary. If you want to work with biologists, get an introductory biology text and read it. If you want to work with psychologists, get an introductory psychology text and read it. Discussions are immensely improved if each party knows the vocabulary of the other party. That said, in my experience, it is unlikely you will be met half way.

7. **Learn how to be empirical and adaptable.** Quite often, the challenge is to find algorithms and formulas that work better than guessing or than the best known method. The proof often need only be statistical and with respect to typical real world cases. In this context, a carefully documented trial of your method under real world conditions will often be considered greatly superior to any kind of paper and pencil demonstration of efficacy.

8. **Learn how to write.** A mathematical worker is a knowledge worker and in large part the currency of a knowledge worker is the manipulation of symbols on a page.

These are my general rules. Please add your own rules and share your own experiences.

The advice in #1 is true and worthwile, but there’s a bit more to the story. It’s very difficult to formulate the right mathematical problem. When someone comes to you with a well-posed problem and asks for a solution, there’s a better than 50% chance that they aren’t asking for what they really want to know. Instead of just telling them the answer to their question, it’s worth investigating in more detail to figure out what they are actually trying to determine.

For example, suppose someone comes and asks you how to do arbitrary-precision computations, since their calculation is losing so much precision that double precision no longer suffices. The easy way out is to tell them that Mathematica or Maple can do this. This answers their question, but it’s almost certainly not the most helpful thing to tell them. Instead, it’s usually best to help them choose a better algorithm: the massive precision loss is a sign that they are doing something they really shouldn’t be, rather than that they should be using much higher precision arithmetic. As an applied mathematician, your job is to help people solve their actual problems, rather than to answer the possibly irrelevant questions they formulate along the way.

Where I agree with #1 is that you should never substitute your own problem for the questioner’s problem. (Just because there’s something else you’d rather solve doesn’t mean it would help them.) However, you shouldn’t feel shy about using your mathematical experience to help them refine their questions or strategies.

Microsoft’s Office Live Students Facebook page has numerous Monster.com articles under the Tips/Advice tab that explain how to apply your experience to a field that doesn’t plainly overlap with your degree. The first step is tailoring your resume towards interesting your potential employer, so I would suggest browsing the articles under the “Resume” column of the Tips/Advice tab. Check out the page at www.facebook.com/officelivestudent

– Jake

MSFT Office Live Outreach Team